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Simplifying 3x(5 + 2x) = 7x + -94 (5 * 3x + 2x * 3x) = 7x + -94 (15x + 6x2) = 7x + -94 Reorder the terms: 15x + 6x2 = -94 + 7x Solving 15x + 6x2 = -94 + 7x Solving for variable 'x'. Reorder the terms: 94 + 15x + -7x + 6x2 = -94 + 7x + 94 + -7x Combine like terms: 15x + -7x = 8x 94 + 8x + 6x2 = -94 + 7x + 94 + -7x Reorder the terms: 94 + 8x + 6x2 = -94 + 94 + 7x + -7x Combine like terms: -94 + 94 = 0 94 + 8x + 6x2 = 0 + 7x + -7x 94 + 8x + 6x2 = 7x + -7x Combine like terms: 7x + -7x = 0 94 + 8x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(47 + 4x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(47 + 4x + 3x2)' equal to zero and attempt to solve: Simplifying 47 + 4x + 3x2 = 0 Solving 47 + 4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 15.66666667 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '-15.66666667' to each side of the equation. 15.66666667 + 1.333333333x + -15.66666667 + x2 = 0 + -15.66666667 Reorder the terms: 15.66666667 + -15.66666667 + 1.333333333x + x2 = 0 + -15.66666667 Combine like terms: 15.66666667 + -15.66666667 = 0.00000000 0.00000000 + 1.333333333x + x2 = 0 + -15.66666667 1.333333333x + x2 = 0 + -15.66666667 Combine like terms: 0 + -15.66666667 = -15.66666667 1.333333333x + x2 = -15.66666667 The x term is 1.333333333x. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333x + 0.4444444442 + x2 = -15.66666667 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = -15.66666667 + 0.4444444442 Combine like terms: -15.66666667 + 0.4444444442 = -15.2222222258 0.4444444442 + 1.333333333x + x2 = -15.2222222258 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = -15.2222222258 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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